Complementarity and Variational Inequalities in Electronics

Complementarity and Variational Inequalities in Electronics evaluates the main mathematical models relevant to the study of electrical network problems involving devices. The book focuses on complementarity problems, variational inequalities and non-regular dynamical systems which are well-known for their applications in mechanics and economics, but rarely target electrical applications. The book uses these tools to review the qualitative properties of devices, including slicers, amplitude selectors, sampling gates, operational amplifiers, and four-diode bridge full-wave rectifiers. Users will find demonstrations on how to compute optimized output signal relevant to potentially superior applications. In addition, the book describes how to determine the stationary points of dynamical circuits and to determine the corresponding Lyapunov stability and attractivity properties, topics of major importance for further dynamical analysis and control. Hemivariational inequalities are also covered in some depth relevant to application in thyristor devices.

Front Cover; Complementarity and Variational Inequalities in Electronics; Copyright; Contents; List of Figures; About the Author; Acknowledgment; Introduction; 1 The Complementarity Problem; 1.1 The Complementarity Relation; 1.2 The Complementarity Relation in Electronics; 1.3 The Complementarity Problem; 1.4 The Complementarity Problem in Electronics; 2 The Convex Subdifferential Relation; 2.1 The Convex Subdifferential Relation; 2.2 The Normal Cone; 2.3 The Convex Subdifferential Relation in Electronics; 2.3.1 Ideal Diode Model; 2.3.2 Practical Diode Model; 2.3.3 Complete Diode Model

2.3.4 Zener Diode Models2.3.5 Empirical Diode Model; 2.3.6 Varistor Model; 2.3.7 Transistor Models; 3 The Variational Inequality Problem; 3.1 The Variational Inequality; 3.2 The Variational Inequality Model in Electronics; 3.3 A General Clipping Circuit; 3.4 A Recti er-Stabilizer Circuit; 4 A Variational Inequality Theory; 4.1 Recession Tools; 4.2 Special Classes of Matrices M and Functions F; 4.2.1 Routh-Hurwitz Matrix; 4.2.2 Positive De nite Matrix; 4.2.3 Positive Semide nite Matrix; 4.2.4 Strictly Copositive Matrix; 4.2.5 Copositive Matrix; 4.2.6 P-Matrix; 4.2.7 P0-Matrix

4.2.8 Positive Stable …